Question

The question is attached with the link​

Answer 1

The sum of interior angles of a polygon =(n−2)×180o

⇒  The sum of interior angles of a hexagon =(6−2)×180o

                                                                           =4×180o

                                                                           =720o

⇒  Measure of each angle of hexagon =6720o=120o

In △PUT,

⇒  PU=UT              [ Sides of regular hexagon are equal ]

⇒  ∠UTP=∠UPT        [ Equal sides have equal angles opposite to them ]

Now, ∠PUT+∠UTP+∠UPT=180o.

⇒  120o+2∠UPT=180o.

⇒  2∠UPT=60o

⇒  ∠UPT=30o

Now, ∠QPU=120o.

⇒  ∠QP+30o=120o.

⇒  ∠QP=90o.

⇒  △PU≅△TSR           [ By SAS congruence theorem ]

⇒  P=TR            [ C.P.C.T]

In △PTQ and △RTQ,

⇒  P=QR          [ Sides of regular hexagon ]

⇒  P

Answer 2

Answer:

The sum of interior angles of a polygon =(n−2)×180o

⇒  The sum of interior angles of a hexagon =(6−2)×180o

                                                                          =4×180o

                                                                          =720o

⇒  Measure of each angle of hexagon =6720o=120o

In △PUT,

⇒  PU=UT    [ Sides of regular hexagon are equal ]

⇒  ∠UTP=∠UPT       [ Equal sides have equal angles opposite to them ]

Now, ∠PUT+∠UTP+∠UPT=180o.

⇒  120o+2∠UPT=180o.

⇒  2∠UPT=60o

⇒  ∠UPT=30o

Now, ∠QPU=120o.

⇒  ∠QP+30o=120o.

⇒  ∠QP=90o.

⇒  △PU≅△TSR           [ By SAS congruence theorem ]

⇒  P=TR            [ C.P.C.T]

In △PTQ and △RTQ,

⇒  P=QR          [ Sides of regular hexagon ]

⇒  P

Explanation: